by Matti Bergström, June 2006
(To be published in form of this text, as a chapter in the book: "The Possible Brain"; all rights reserved)
Abstract: Based on empirical findings of our research on brain as a system, the concept of time in our behaviour, subjective and objective, is analysed. The imaginary mode of time, covering functions of the primitive brain stem, is treated according to Hawking´s description, and the real mode, covering functions of the highly developed neocortex, is treated as it is used in physics. It is introduced a third type of time that is based on how these two modes interact in the function of brain, in the neuromental Self, situated in the limbic system, between the primitive and developed part of the brain. The result of the analysis shows that the interaction of the imaginary and real time in the complex space of the Self results in a time function that is called the "complex time", and that this mode of the time function forms our fundamental reality in which we live. Therefore, only the real, physical time or only the imaginary, mental time, used in the research of our world separately, are one-sided aspects of time and can not cover functions of the whole world. In order to cover them all, we have to use the complex time. The concept of complex time also helps us to understand in a new way the mind-matter problem, and also the "observer-observed" relation in physical experiments.
Basic facts
The brain can be treated as a system (Bergström 1969, 1997) so that it has two poles, one primitive entropic, chaotic pole in the brain stem and one highly developed negentropic, ordered pole in the neocortex. The signals of these poles meet in the limbic system (MacLean 1973) forming our neuromental Self (Ikonen and Bergström 2004). This Self can be described as a 2-dimensional orthogonal space with one real number dimension (r, outer information, knowledge) showing the input from the order-pole and the other imaginary number dimension (i, inner values, belief) showing the effect of the chaos-pole (Bergström 1964). The Self space accordingly is a complex number space, the dynamics of the space vector
(1) c = r + b i
where r and b are real numbers and i is the imaginary unit, exhibiting the balance of the two inputs to the system. The vector movement is covered by the imaginary time (ti) controlling its movement from the i-dimension (our inner feelings and values), and also by the real time (tr) controlling its movement from the r-dimension (the outer physical world). So the time course of the complex vector in the complex time (tc) directs the processes of the neuromental Self. These processes are either conscious (r-content) or subconscious (i-content) or they consist of these both (i,r-content). Thus:
(2) tc = f (ti, tr)
If they consist of both, then they have in the (i,r) plane of the space a projection on both the i- and r-dimension. The complex-vector is now situated in the (i,r)-plane in which case both conscious and subconscious components take part in the function of Self (see below).
One could ask what kind of a force is acting in the (i,r)-space of the Self in brain, that results in the movement of the complex vector?
For this, it has to be noted that there exists in the brain an entropy difference between the stem and cortex (Bergström 1969). This results in a force acting towards an even distribution of entropy and balance in the whole brain. The force is acting at the border, the limbic Self, between the entropic effects from stem and negentropic effects from cortex, the border acting as a barrier against an even distribution of the entropy. It is this force that causes the dynamics of the complex vector in the Self space (see later). The maintenance of the difference in entropy between the two poles of brain needs a continuous input of neural energy from the sensory channels to the both poles (see later on the specific and nonspecific sensory channels).
The "Force field" of the complex space of brain´s Self can be considered as corresponding with the force field that David Bohm sees as a characteristics of the Schrödinger Wave function (Bergström, Ikonen 2006) and that acts in the whole world guiding the subatomic particles, This, since this wave function has an imaginary and a real component, as is also the case with the complex vector function in brain´s Self !
In a simulation of ideal neural networks (Bergström and Nevanlinna 1972) where the distribution of neural energy (electrical impulses) was calculated for a given system, it was found that if the environment works upon the system, causing a state of non-equilibrium in it, then it renders possible the performance of work (behaviour) by the system back upon the environment. In the calculation of the so-called canonical distribution it was observed that the mean firing frequency of the electrical impulses (energy) in the system obtains a position in the formalism similar to that of the temperature in statistical mechanics. In a closed neural system the following approximation for the entropy (H) was found:
(3) H (E,n,N) = 4E/nN (1 - E/nN) (n - 1) log (N + 1)
E = total energy, n = number of neurons, N = number of branches/neuron
In the following it is shown how the force of the Self moves the space vector resulting in the process of thinking of the Self.
Application on thinking
We have used the characteristics of the Self space for showing how the process of thinking occurs in it (Ikonen, Bergström 2005). In considering the space being a fractal Mandelbrot space (Bergström 2001, 2005) the Julia equation can be applied:
(4) Zo^2 + C = N
where C describes an external stimulus invading the (i,r)-space of the limbic neuromental Self and taking a fixed position in it, and Zo describes the response of the Self to this "strange invader", with capacities concerning both subconscious (i) and conscious (r) actions. If so, then the vector of the response (of the form a + bi, a and b being real numbers and i an imaginary unit) begins to iterate in the space. We have developed a computer program that shows the coordinates of the iteration and also a semantic expression of it containing the concepts of "knowledge" (r) and "belief" (i) of/on the strange stimulus (physical, sensory stimulus or a proposal made by an other person). We have also added for these purposes a third orthogonal dimension to the Self space, a dimension of possibilities (p) denoting the effect of the primitive part of the limbic system itself on the thinking process (Bergström and Ikonen 2005), by way of emotions contained in the abiliy to phantisizing freely about the invading stimulus/proposal.
More than 50 subjects are tested, men, women and children, with this method, the results showing different modes of thinking (Typology of thinking, Bergström 2002) in different subjects. The results can be interpreted also in relation to the type of time factor (ti, tr, tc) used in the thinking: in children the imaginary time (ti) prevailed, in men the real time (tr). Women showed both types (tc). The type of thinking in the children occuring mainly in the imaginary time, also exhibited a great amount of possibilities, thus showing that they were phantisizing and using an imaginary, non-directional, simultanous type of time, while going on with thinking in the linear, physical time. An interview after the test (performed with all subjects) could show this (Ikonen, Bergström 2005).
Thinking in the imaginary time can help the thinking in the real time, which proceeds with its mathematical logics. It is known, that in this mathematics the imaginary unit (i = square root of -1) is an obstacle that prevents certain calculations. On the other hand, we know that
(5) i^2 = -1
which means that when the imaginary numbers in the subconscious, imaginary mental sphere in our mind are interacting (multiplied with each other), it is resulting in negative numbers. These negative numbers can be filled with positive numbers and used in real time thinking and mathematical logics. This, since the negative numbers can be considered as a kind of "places", squares with the sides (i), where unconscious contents can be placed and forwarded to the real, conscious sphere. In that sense, problems, where logics does not help, can be solved in our imaginary subconscious mental world with its holistic, free fantasy-thinking (also free discussions, as suggested by Bohm, between people can help here), that is not restricted with any rules. This can also explain why problems in waking state can have a solution during sleep and during dreaming. In this connection it is good to see that the mental states can be understood as "macrostates", whereas the physical material states are "microstates" (Bergström 1967, 1972, 1986). The interaction between these states is in brain possible only in the complex number space of the neuro-mental Self, which space is the (primarily empty) border between the conscious and subconscious worlds of our brain.
In order to investigate the space of the pure imaginary, subconscious world in the brain, of which the i-dimension of the complex (i,r)-space is a sign, we have to look at the intrinsic characteristics of the imaginary numbers. They are, after all, what our world is also about. That the imaginary number is equal to the square root of (-1), is only an aspect from the physical, conscious side of brain on the imaginary world. And the conscious, logical mathematics can not understand this square root of (-1). Nor can our logical thinking understand what is behind this border, of which this square root is an expression.
We have to begin with the equation (5), which states that combinations, i.e. multiplicative products of imaginary numbers, result in negative numbers. We could now look at the border between the conscious and subconscious from the inside, that is, from the subconscious world aspect. Then, behind the border appears to be a world of positive numbers on the real side, whereas the subconscious world itself consists of negative numbers. For the subconscious thinking this possesses no problem, since the negative numbers can easily be filled with the positive ones. The real world is then easily conquered with the subconscious thinking, whereas the imaginary world can not be conquered with conscious thinking. And so it is: we can easily translate our phantasy and dreaming to real language but not the real thinking to fantasy or dreams. These latter appear on their own basis and values, or axioms. The values can be translated to conscious language, where they appear as axioms, e.g. in logics and mathematics. This effect of the subconsciously working brain we have called "enaxia" - an axiom producing force (Bergström 1989) - that determins the axioms for treatment of information (negentropy), which information gives structure to the the energy that is mediated to the environment by the individual. Thus we have for the behaviour B
(6) B = V --> I --> E --> M ,
where V is the Enaxia (value) force, I the Information (negentropy), E the Energy and M the target matter. According to this, we should also in physics use the method of describing the reality as the chain
(7) Enaxy --> Entropy --> Energy --> Mass
This gives us at hand the possibility to change the i-dimension of the complex space to an i-square dimension, so that the complex space vector is a real vector
(8) c = a + b i^2
or, in form of the subconscious negative numbers of the imaginary world
(9) c = a + (-b) = a - b
The vector now shows the balance between the inner world of our brain and the outer world simply as a difference where the inner is subtracted from the outer. And this is what it is: the unconscious "knowledge" is missing from our conscious knowledge! What really would be needed, is a new kind of "logics", a complex form of it. In fact, the "complex thinking" that was presented above, could be a good starting point in doing it. Then, also, the "enaxia" effect from the subconscious brain would be taken into account. But, to do all this, is a concern of mathematicians.
Imaginary world in brain
We have to take seriously the fact that mathematics has shown us that there excists a "hidden world" (see also David Bohm), a "missing part" of the reality, behind this strange number, square root of (-1).
We have to ask, what kind of physiological functions are involved in the human brain in its imaginary world? This, in order to be sure that the space of the limbic neuro-mental Self, that is presented above, has a physiological foundation.
The imaginary i-dimension in this Self-space described the input from the deep, primitive brain stem, whereas the r-dimension described the input to this space from the neocortex. Thus, the imaginary world and the brain centres responsible for it was the first to develope and mature in the ontogenesis. But, as we know, all earlier centres are still there in the wholly matured, adult brain. So the "imaginary centres" - as we might call them - are still functioning in the mature brain.
The developmentally primitive centres we are talking about are those of the embryonal time, when the embryon was freely floting in the uterine fluid (relative weightlessness). Since no centres for the gravitatory effects were developed at that time, the embryonal brain did not have any sensations of the planetary world, that is, the up-down or weight. The gravitatory centres mature only later, at the 7 - 8 week after gestation. Until then, their brain did not have any input of the kind as the Self in the mature brain, that is such as represented by the r-dimension of the Self-space.
It is natural to assume that the embryon did not have any sense of the real time (tr) either, since it did not have a sense of any motions in an environment with gravitation. The sensory systems for registering the physical environment were not yet there.
As refered above (Bergström 1964), we could show in psycho-physical experiments that as soon as the subthreshold limit of the stimulus magnitude was reached, the subjective mental experience was to be described with stimulus quantities that included an imaginary number (square root of -1). The subthreshold limit is that limit where cortical sensory centres do not act and where the subconscious mental state begins to function alone. This empirical finding can be interpreted so that the subconscious state of the brain is an "imaginary state". This is a state where the cortical centres do not function and where only the brain stem centres are active.
This supports the view that the embryon lives in a time that is the imaginary time (ti). In the space of the self, the (i,r)-space, this imaginary time meets the real time (tr), thus forming in the complex number space a time that we call "complex time" (tc). This occures only later on when the cortical centres mature.
Why three forms of time?
It is interesting that Hawking consideres the possibility that it is the imaginary time that is our "intrinsic real time" and that the physical time which we call "real" is there only for registering outer, physical processes of our environment.
Looked at from our brain physiological point of view, Hawking is right !
This, since what we, our internal us, are, is the "human mental brain" with our own values and our own internal feelings and attitudes. We are not our "scientific brain", that is there only for registering the state of our environment, so that we, our "human us" can live at this our planet! How we succeed in this, is shown by the state of the complex vector in the complex number space (p,i,r) of our Self. To this state we are reacting with our thinking, as shown above.
The imaginary world and time of our brain is seen in pure form in children, up to an age of 5 - 6 years. The young child is mainly subconscious in that its behaviour is controlled mainly from the deep brain stem centres. It looks at its situation in the environment as a whole, and is not so much concerned about the details in the environment. The subconscious state is holistic and can be understood as a macrostate of the brain centres being in action. The child lives in its feelings and evaluations, dreaming, fantisizing, playing and being interested in fairy tale characters that it sees also in the environment in shadows and darkness. All these belong to the imaginary world of brain. The cortical centres are not that much present.
What is interesting and typical about children brain, is, that it contains in the limbic areas great amounts of "clouds" of different mental contents, that are the stuff that is freely treated in the fantasy: the "possibility cloud", as we have called it. This is why the child in its thinking sees much of possibilities (see above) of how to react towards strange "invaders" to its Self. This is where the fantasy acts, without any logical rules. All this belongs to the imaginary mental sphere of brain. All of this also belongs to the imaginary time that is independent of the physical, real time (it is orthogonal to this real time, according to Hawking). The imaginary time is a simultaneous time, not having any extension in the the linear, real, physical time. It is like a "cloud on the sky", while the child is proceeding with the clock time (see later about clocks). It is good to know that the word "tempus" originally ment "opportunity", and in this sense "possibility". The possibility cloud is apparently "simultaneous time" (ti) filled with huge amounts of possibilities to be realized in real time. That this time is our factual, "intrinsic real time" (and not the physical time) is shown in that we are counting time backwards, as "... 3, 2, 1, NOW! ", if we estimate time in some important situations when an important decision has to be made, and how many possibilities are left.
It is apparent that our artistic activity, despite the technical performance of the artwork is in the physical real time, occurs in the imaginary time with its possibilities and creative ideas. As expressed by Kandinsky, the first "abstract" painter, art is not communication between the artist and other people, but a communication between the artist and his/her inner being. This would mean, with our concepts, that art is a communication between the real and imaginary world. In this sense, we have (Bergström, Ikonen 2005), in consulting advanced artists, "dressed" the coordinates of the pir-space with colors, and also with tones (that were suitable for expressing the dimensions) e.g. blue color/march tones for r-dimension, red/religious tonality for i-dimension, yellow/tonal improvisation for p-dimension), in order to letting the computer-programmed Self paint/compose an artwork. In this, the test person was given a color/tone-sequence and had to give a spontaneous color/tone answer, after which the program performed its task in form of complex-vector iterations. The coordinates of the iteration were then displayed with colors/tones, resulting as a painting or a composition. This could then also be compared with the thinking, the semantic text of it.
Application on physical observation
The presented function of the brain´s Self space explains certain problems in physical observations. It is known that in observing subatomic particles there occurs a non-predictable "dance" (the word used by late David Bohm) of the particles so that their exact position in local space can not be determined. From where does this dance come? Yes, since the actual observation is realized in the complex space in the Self of the observer, there is a "dance" in the form of the iterations of the object in this space. The projections of this iteration of the complex-vector appear as a local "dance" on the r-dimension of the pir-space. The dance thus occures in the complex time (tc) of the observer´s Self and its origin is not in the real time (tr) in the physical environment, but in the value-loaded imaginary time (ti) acting on the complex time (tc)! It does not help in saying that the dance is there also in case of pure instrumental recordings, since the instruments are constructed by the thinking human observer. According to Cotterill the thinking is there in order to prepare a motor planning, so all planning of instruments is covered with thinking - and thus also with iterations - and dance!
The dance of the subatomic particles in physical observations is due to the thinking in complex time in observer´s brain. If observations could be performed only in imaginary time of the brain´s Self of the observer, then the dance would not be there, since the imaginary time is simultaneous. Observation is, however, not possible in this manner since the cortical sensory areas would not function. Only with the "lower" senses like smell, taste, and sertain skin receptors (they could be called "imaginary senses") are observations of the outer environment in this situation possible. Observation in only the r-dimension is not possible either since the brain cannot work without being "aroused" to full consciousness from the brain stem.
On the other hand, the connectedness of the particles, that the physicists talk about as a problem, can be explained with the imaginary time as a property of the complex time that combines the "dancers", the particles, to a simultaneous whole.
But there is another problem in physics still to be solved: the Heisenberg´s "Uncertainty Principle" (1955), which states that a particle´s time and energy or location and velocity can not be observed simultaneously. Also this can be explained in brain (Bergström, Ikonen 2006), in the complex number space of the limbic Self, with its real time dimension (tr) and imaginary time dimension (ti). If a particle is observed at a certain location at a certain time (tr5, say), but at the same time instant the complex vector, iterating in the complex space, crosses the projection of (tr5) in negative direction of time (tr), e.g. from (tr8) to (tr2), then the complex Self observes the particle, not at the time (tr5) but at the time (tr2). This means that the physical real time (tr) proceeds backwards with a lag of a time span (5 - 2 units time = 3 units time). This is possible since the complex vector uses imaginary time in crossing the projection of the time moment (tr5). And imaginary time itself is orthogonal to the physical time.
t is interesting that Heisenberg himself thought that the physical time probably moves backwards, when very short time intervals are observed, and that our view on causality is not the right one (Heisenberg 1955). Here again, thinking - its imaginary, subconscious component - in observer´s Self affects the observation, now of the physical time (tr). This is "uncertainty", that Heisenberg meant, but there is an explanation of this phenomenon, if the brain of the observer is included in the process of observation. Heisenberg himself wrote: "What we observe is not the nature itself, but nature exposed to our method of questioning". The "nature" appears in the observation situation as a content of the physical, real time (tr). The "questioning", on the other hand, appears in the brain as a content of the imaginary time (ti). This, since the i-dimension of the Self-space describes the input of value-contents from the deep brain stem, i.e. of what we ask to know about the nature. So the nature is exposed to our “questioning” (evaluation) in the process of observation.
It seems that the DEVELOPMENT of PHYSICS from the Newtonian to the subatomic mode, followes the same principle as is the iteration of the Julia equation (describing our thinking): FROM NEWTONIAN WHOLENESS to SUBATOMIC FRACTALS !
There then appears to be a paradox: a "sleeping physicist" would be the best, ideal, observer, since the imaginary, subconscious dimension would not affect the cortical/sensory functions and the results of our observation in physical experiments. There would be no iterations in the observing Self. And no local "dance", nor uncertainty, in the observed object.
In fact, as shown by Jauhiainen (1969), the level of arousal producing the consciousness, has an effect on the estimation of the quantity of the physical stimulus in psycho-physical experiments. This "Vigilance-factor" acts on the content of the complex time (tc) in the complex space of the Self through the i-dimension, that shows the effect of the brain stem, the source of the arousal. In the case of a variation of the stimulus the factor compensates for the variation so that a constancy of the stimulus is reached. This is conform with what we have presented above about the "sleeping physicist".
It can be seen that these problems in physical experiments can be explained on the base of brain facts.
Interaction of 3 forms of time
In having had discussions with David Bohm, I have learned that his explanation of the dance-phenomenon was much alike with what we have described above, in spite of that he founded his concepts on Schrödinger´s wave function. This function contains "hidden" information which acts upon particles so that their movements cannot be wholly determined by their local interactions. His term "non-local" points to our imaginary dimension (i) in the Self space, and "local" to the real dimension (r). Also, the "empty route" from the wave function to the observer, that does not leave any physical signs, but is affecting the result of observation, can be explained with the simultaneous wholeness of the imaginary time (ti), operating in the brain stem and covering the whole observing system. Physiologically, for this there exists the so called "non-specific" sensory route from the observed object directly to the brain stem, that does not leave any detailed signs of the object.
Apparently the wave-particle dualism in physics depends on seeing the imaginary time (ti) and real time (tr) as separate forms of time. If they are treated together as complex time (tc), this dualism can be avoided. In his "New theory on mind and matter" (1990) Bohm states that to the last end mind and matter are not sepated, but forming the same common process. This is just what we have presented above: they are the same phenomenon in the complex time in the (i,r)-space of brain´s Self, because "mind" points to the imaginary dimension and "matter" to the real dimension, which dimensions form the complex time (tc). So also with mind and matter, they are the same phenomenon (Bergström, Ikonen 2006)!
There only remains the question how to "measure" this common process? In each physical object there has to be measured its complex features. This contains its locality and time, and its weight. These are what we usually call physical measures. But we have to measure also its imaginary measures. These are the values and the possibilities. The question is how we should do it? The principles of this measurement are that the object is related to other objects, which gives its value, and that the object´s possible effects should be specified, which gives its possibilities. Of course, the value can be given as the price of the object, and the possibilities as its possible effects on a scale of "good-bad" effects. Take an atom-bomb: it has a weight, a local and time extension, a price and a bad effect (for time being). An air-bomb, again has also some weight, local and time extension, but a lower price and not so bad effect (as atom bomb). The units for measurement can be investigated and agreed upon for these imaginary characteristics. In economy, with our money, we are doing this kind of measurements.
Only in this manner we can get the measures of all objects in our environment, that gives a complex result, that is, both the real and imaginary characteristics of an object. In fact, we are, subjectively, doing such estimations ("measurement") of all things, their imaginary characteristics, in our environment in this manner. Only that it should be agreed upon a common scale in which we do it (like we are doing with money, price and value of things). And this we can find. This is something that the physicists and the psychologists can do together!
The fact that conscious and subconscious functions appear simultaneously in the function of the Self seems to be problematic. The problem concerns, however, only the psychological view of the concepts. If the participating physiological brain functions are taken as a base of the concepts, then the simultaneity is natural: for consciousness with its cortical activity (sensory contents, logical thinking etc.) the brain stem arousal is needed (e.g. the "Jauhiainen-parameter", presented above), but for subconsciousness with its brain stem activity (internal feeling, values etc.) the cortical activity is not needed. In this sense the complex time (tc) is a possible form of time function in the (+i, +r)-plane of the Self space. In the Typology of thinking (see above) this form of thinking in the (i,r) plane was called "Understanding", since it combined knowlege about outer information (r) and belief on internal values (i) of an actual situation of the individual in its environment. "Understanding" is a concept that comprises the individual itself and its environmental situation as a whole! This we can see in the Finnish word for "understanding", which is "ymmärtää" that means "surround", "see the whole". And "Wholeness" is a characteristics of the mental contents of brain stem functions, whereas "elementary" is a characteristics of the mental contents of cortical functions. Finnish language is in a sense a primitive language that describes the nature in a direct, natural way.
In the concepts such as "consciousness" and "subconsciousness" we are, e.g. in consciousness research, mixing the psychological and physiological meaning of the words. This causes much of trouble in this kind of research. In this sense a treatment of the brain´s Self as a border between brain stem and neocortical effects, and describing the space of this border as presented above, could help. This because concepts decribing the brain as a system combine psychology and physiology in a natural way. Systemic-mathematical concepts as used here, are "neutral".
By the way, thinking in the (+r,-i)-plane of the Self space was called "Perfectionistic", since it considered only detailled logics without any consideration of the value contents of the object of thinking. Thinking in the (-r,+i)-plane, again, was called "Fundamentalistic" since it considered only the value contents of objects of thinking (like in religious fundamentalistic people) without taking care of any factual information about this object. A "Confused" thinking took place, if it occured in the (-i,-r)-plane, so that no logics or value contents were present.
It seems that we can understand the concept of "Time", in a new way, if we look at it on the background of the primarily empty Self of the brain (a border is mathematically always "empty"). Our concept "empty" stems from the sensory experience of the outer environment, that can be empty, "there is nothing". If so, then the the cortical sensory area in brain is empty. But the brain stem content is not empty: it is there feeling the emptyness of the sensory field of mental contents. It also feels that there are possibilities for things to appear in this sensory, conscious field. So, emptyness contains always possibilities! And possibility is time, simultaneous time (ti), as was considered above. It follows that the intrinsic meaning of time in our life is that our life is "Possible"! We have the freedom to choose the possibilities, as do the children, "experts" in development and expansion - with their "Childbrain" (see Bergström and Ikonen: "Our three brains", to be published). If we have this Childbrain spared (if the "information-school" has not inhibited its function) we can live with this time, without being restricted to live only in the physical logic-linear time. Whoever created us, gave us an empty Self, a potential with huge amounts of possibilities. In fact our brain is not a material construct, nor a mental world, but a "Possible Brain" (a book we are working on).
There is an interesting thing about the third form of time, the complex time (tc) in our brain: in being the sum (equation 8) of the imaginary time (ti) and the physical time (tr), then it can be shown that this complex time is a "Potential time" that does not move in any direction but only contains the imaginary and physical time as possible functions, which it can release. Consider a process for something that has to be done, then we can start a timer clock at the beginning, the moment 0 of the process, and let it run counting how many possibilities are left until we have to do what has to be done. This timer measures the imaginary time (ti), backwards. At the moment 0 we can also observe a usual physical clock and measure the time (tr) from this moment to the end of the process. Putting this together and calculating the complex time sum (tc) of (ti) and (tr) we get:
Imaginary time (ti) with timer: begin 5, 4, 3, 2, 1, 0 "Now!"
Physical time (tr) with a clock: begin 0, 1, 2, 3, 4, 5 "End!"
Complex time, the sum (tc = ti + tr): 5, 5, 5, 5, 5, 5 "Constant!"
(ti) shows how many possibilities are still left to be used, and (tr) shows how many possibilities are lost. This is the intrinsic meaning of the imaginary mental time (ti) and the real physical time (tr). Children, up to about 5 years, do not understand clock time, the physical time (tr), but only the mental time (ti). This is because the sensory cortex is not yet fully developed to differentiate physical processes in the environment. Children´s interest in time is to wait for things to happen them, that are important and interesting. They, so to say, live in their future and create possibilities (ideas) contained in it: they live for developing them selves and to grow to an adult age. They use for this the imaginary time.
Complex time is a sum of the imaginary and physical time and thus a "POTENTIAL TIME" that does not change or move but being constant and including the two other forms of time. From this Potential (the "Now" of Bergson 1992) the " I " can choose to use more of the physical or more of the imaginary time to move in, depending on the situation in which it is, related to the inner feelings and values on one hand and to the physical environment on the other hand. If there are problems on the mental (imaginary) side, then I choose imaginary time, if there are problems on the physical (real) side, then I choose the physical time. If there are no problems, then the " I " only is. The " I " is the head of the thinking (iteration) arrow, the complex vector, and the thinking shown by the dynamics of the vector prepares for a plan (program) for actions of the individual (Cotterill) and selects the right form of time to be used in this action. As to the content of the complex time, that does not move but being constant (the "Now"), it can be assumed that it has access to the concepts of what it has learned from experiences in the imaginary and real, physical time. This since concepts are regarded as "lifted from time" (Immanuel Kant), that can be understood as meaning "lifting from the moving time" (ti and tr). And, after all, the important centres for memory (a static storage) are in the limbic system, the same area of brain where the Self is! The "lifting from time" can mean lifting from the dynamic (ti) and (tr) to the (tc), the static complex time.
As to our experience of time, it has to be noted, that if nothing happens in our inner mental subconscious world or in the outside physical environment, then there is no flow of time. There is only the experience, in the complex space of Self, of "present", an experience without any time characteristics, but only with pure existence (a pure "Now"). There is nothing mysterious about this "existence": its only content is a huge intensivity, POTENTIAL, a possibility for thinking and acting in imaginary and/or real time and world. It is a spiritual power for us, to be used in our living. It is simply "Me", that does not change. It is like my Name, that does not get older with the physical time. It is as young when I die as it was when I got my name. This Name is "lifted from time" (Kants definition of "concepts" living their own timeless life), from the physical time to the complex time, to be the name of my Potential that I use during my life. I inherited this Potential from the period of life before I got my name, and before the centres of gravity in my brain were matured, from the embryonic life in relative weightlessness without planetary space or time.
This Potential is the base of all forces in nature, the macroscopic as well as the microscopic, the Newtonian and the subatomic forces. In order to show this, we have only to specify, in physics, the imaginary and the real time processes and the complex world between them. For this, the Hawkingían theories about the imaginary time and world, and the theories of the ordinary physics have to be combined to a whole, a theory of the true, ultimate reality of the complex world.
So, the struggle of what time is (see e.g. Paul Davies 1983, 2006), can be ended. After all, the structures in our brain, that are connected with the experience of time, are in (or connected with) the limbic area, between brain stem and cortex, the same area as our neuromental Self and its complex space. The most important centres (Damasio 2006) are the hippocampus (forming of new memories), temporal lobe (retriving memories) and basal forebrain (identifying the chronology of past occurrences).
It is here good to think on Einstein´s cosmological model (1917), that presented a timeless, static aspect on the universe. Such a model is conform with our concept of the complex time (tc), which is static and "timeless", since it is a pure Potential containing the imaginary, mental time (ti) and the physical, real time (tr) only as possibilities. Our brain has been developed for being able to use these possibilities in order to preserve the Potential of our universe. This, it seems, is the ultimate cause for us to live in our mental and physical time. The universe, after all, is a huge Potential! So its ground state can be static and timeless, and there is no need for it to have a beginning or an end (see Hawking´s model of cosmos). It is only the physical time, one of the possibilities of the cosmic Potential to act, in which "beginning" and "end" can be realized, in order to govern the material side of the universe.
So far, the "Big Bang" (BB) as a beginning of our universe, a concept of cosmologists, results from the use, only of physical time in their research. Hawking´s model of a universe without any beginning or end, again, results from the use of the imaginary time in this research. Our model of the universe as a Potential, resulting from brain research, does not need any concepts of beginning or end, nor of any mental or material side of the universe. The only concepts resulting from our model are "Potential" and "Possibility", which do not need any "beginning", "end", "mental", "material", or "time". Our concept of "complex time" for the Potential of brain´s Self, resulted from the treatment of this Self from the aspects of imaginary (mental) and real (physical) time. This we have done in order the scientists (psychologists and physicists) could undestand the meaning of the concept "Potential". It has to be noted that it is NOT a scientific concept of the ordinary, classical science. Since it is timeless it can be understood as a "presence" (see above), an everlasting "Now", a concept that Einstein was worried about and considered to be different from past and future and outside from the topics of science. And so it is. It represents the True reality behind our mental and physical being, that we cannot penetrate, but can only use the Possibilities it creates for us to be able to live. It can also be understood that in spite of not being time, this Potential is the origin of time: the original meaning of the word "Tempus" is (see above) "opportunity", so time is only one of the possibilities this Potential can create. "Understanding" - that is needed here - is not equal to "Knowing": it is much more. It is Knowing and Believing, together! So it containes both real and imaginary time and concepts (see Bergström, Ikonen 2002 on "Typology of Consciousness" and of "Thinking").
In the Western countries we are occupied with problems in our environment, in the physical nature (ecology, economy, wars etc.). Therefore we are using the physical, real time (tr), and almost forgetting the use of imaginary time (ti) and problems of our subconscious mental being (mental disorders, depression, problems with children and youth, stress etc.). We are also forgetting to use the most valuable of the possibilities of the Potential contained in our Self. It seems that one of the most valuable activities in that direction, are the religious ones. Our belief on God, combined with knowing the world, can be considered as opening the way to new spheres of life with new possibilities, different from the physical and psychological ones. Belief and Knowing together (see above) makes us to Understand our world. No wonder that Augustine said that "Deus est possibilitas" (God is Possibility). And in theology it is stated that we cannot know what God is, but only what He does to us (see Matti Bergström "Neurotheology", a manuscript that will be published soon). Dennett (2006), discussing the relation between religion and science, thinks that religion needs also scientific knowledge. But this cannot be true, since in our brain belief (relation of limbic Self to deep brain stem contents, such as the religious contents are) does not need knowledge (relation of this Self to cortically mediated environmental contents and functions). On the contrary, cortical, and scientific, activity is not possible without brain stem activity, so, instead, science needs religion! It is good, here, to remember what master Eckhart, the famous mystician from middle age, told about experiencing God: the Self has to be emptied from knowledge, only then can God be experienced by us (the "Gottesgeburt").
Gravitation and clocks
There also is an interesting thing about the gravitation: in brain´s Self, the complex number space. The physical phenomenon of gravitation is shown on the real (r) dimension, whereas a counteracting force, that we can call "anti-gravitation", is shown on the imaginary (i) dimension (the physiological arousal from the brain stem). When they interact forming a complex phenomenon (i,r), there is a balance between these both, which means that the individual can move in the physical environment in the complex time freely in upright position without being too much concerned of the planetary gravitational force. It is obvious that a freedom from the gravitation stems from the embryonal developmental time (see above) when the embryon lived in the fluid in relative weightlessness, in the imaginary time, and when the gravitatory centres of the brain were not yet matured.
Also, the early developed brain stem, with its entropic (chaotic) signal streams upwards the brain to the limbic neuro-mental Self and cortex, wakes up (arousal) these areas of brain to a conscious state. This arousal counteracts the gravitation: the i-dimensional effect of the complex space, that according to equation (3) corresponds to temperature in material physical systems, is antagonistic to the gravitational effect from the r-dimension of the complex space of the Self. The relation between these effects corresponds with August Comtes view (see Prigogine, Stengers, 1984, p. 104): heat and gravity coexist in physics, but are antagonistic. This shows that physical problems can be solved in the observer´s brain, in the complex space of its Self. Also, Einstein´s interpretation of gravity as "space curvature" can be understood from this point of view, since the r-dimensional effects on the complex (i,r)space are allways "distorted" by the i-dimensional effects, and vise versa. The "curvature" by Einstein is such a distortion. This interaction between i- and r-dimensional effects in observer´s brain has to be introduced into the physics in order its research and theories to be targeting on the fundamental, true reality, that exists, not in physical time, nor in imaginary time, but in the complex time.
Also, theories about the universe being a fractal world (see references in: Marcus Chown, "Fractured Universe", New Scientist, 21 August 1999) are conform with our view that the true reality is in the complex time. This since this reality, being a complex reality, is a Mandelbrot set with a fractal structure. The use of only physical, real time, without any notice of the imaginary time in describing the universe, is an one-sided view (see above) resulting in erroneous theories.
It is known that there exist in children disorders that make them feeling a constant pressure of this physical gravitation so that higher motor and cognitive functions do not develop in a normal way (Niklasson 2005). They can be helped with a therapy that consists of normalizing their early mental and motor behaviour, thus including their imaginary and real world, i.e. to live in the complex time. It is possible that the difficulty in physics to cope with the gravitatory force would be solved if the "complex gravitatory phenomenon" would be taken as fundament. Freely spoken, physics seems to suffer of the same disorder as the above mentioned children: it has not yet reached its highest "cognitive " level and needs a "therapy" in which it has to repeat and "normalize" the early fundamental thinking including the imaginary, basic mental values. One example of that this is not done, is the above described statement of Dennett about the relation between religion and science, that religion needs science. Correction of this kind of thinking, by many physicists, could help physics to solve its problems (e.g. of gravity!) and develope further to a mature state.
There is an interesting problem of our clocks measuring the time: there should, according to what has been said above, be 3 types of clocks for the three types of time!
Our usual clocks are measuring the physical, real time, that is uni- directional and sequential. But what obout the imaginary time, and the complex time? The imaginary time clock should measure a simultaneous time, where we can move forwards and backwards, according to Hawking. For this a timer clock can be used (see above). Without going further in this problem here, it can be stated, on the base of brain function, that this clock should measure the state of functions of the brain stem, the i-dimension of the complex space of Self. Since the brain stem contains regulative centres of our whole organism and controls the simultaneous state of this organism, the evaluation of our internal feeling and development of this evaluation (moving forwards and backwards) would be what this imaginary time clock also should measure.
The complex time clock, again, should measure the combination of the real and imaginary time. Since this combination occures in the Self space, this clock has to measure the state of the Self. This has to do with our well-being and the satisfaction with the situation of our life as whole. It should measure our spiritual Potential.
In fact, we are in our every day life thinking on how the simultaneous state of our whole organism developes, and feeling and evaluating our internal state. So we have an internal imaginary time clock. It would not be impossible to register this state in some way in a suitable mode!
The same holds for the complex time clock: only that it should register the state of our Self and its well-being, its "potential" (see above!).
As we have developed, on empirical foundation, a view of the brain as being composed of three brains - a man brain (the left), a woman brain (the right) and a child brain (brain stem), the three clocks could be named as 1) Man clock, 2) Woman clock and 3) Child clock. This, since the three modes of time and their measurement correspond with the characteristics explained above. The theory of our 3 brains (Bergström and Ikonen) will soon be published.
Conclusion
All this shows that there exists a "True reality", in which we live, a reality, where there is a COMPLEX TIME in which things are and proceed. It also shows that using only the real time in physical observations does not work: it gives a wrong picture about our physical world around us.
In taking into account the imaginary time and with it the characteristics of our subconscious mental world, so typical in children, there can be opened a gate to a - presently missing - hidden part of our world, the imaginary world. This, together with the physical world, would be our factual World we are living in, in our environment, the TRUE REALITY ! This reality proceeds in the complex time, a sum of the imaginary and real, physical time. This result of our analysis is supported by the fact that it explaines the difficulties in physical experiments, where there exists an "uncertainty" of the observation of subatomic particles. It could be shown that the difficulties depend on the use of the wrong form of time in observer´s brain. The conclusion was made that a selection of the right form of time - imaginary, physical or complex time - is needed for different situations of the individual in its inner, mental and outer, physical environment. This, in order to solve problems that are related with our life in these environments. The use of the physical time, as it would be the only form of time, is considered to be caused by the great problems we have in living in the physical world around us. This makes that we are not aware of the increasing problems in our inner mental world. For this the use of imaginary (and complex) time would be necessary.
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