In the template we introduce the dichotomy tree; a binary tree that emerges when a dichotomy is taken beyond the one:one, EITHER/OR form. From this we see that a 'rule' emerges that says 'you cannot cut the whole'; any dichotomy is in fact the manifestation of a continuum and the process of dichotomous analysis enables the development of refined models of that continuum where we move from EITHER/OR states to BOTH/AND states. 'Meaning' emerges from this process but is in fact only valid within the context of dichotomous analysis and is therefore 'relative' rather than 'absolute'; it is an aspect of dichotomous analysis. However, if our use of dichotomy stems from it's neurological internalization than it is possible that the 'meanings' we make do have some value outside of 'us'; they are to a certain degree 'objective'.
So far we have delt with 'mind' within the context of mathematics and psychology as well as the possible neurological aspects. But what happens when we look out into the universe?
To start with, we can review the properties of
dichotomy
We can add to this the concept of concensus mapping, where, when making
maps of reality that can be read by many people, there is a need of agreement
on symbols and their meanings. The use of dichotomies based on extremes is
common and the map is built dichotomously-derived layer by layer (e.g base
layer is land/sea. Next layer, considered to be within the context of the
previous, is high/low etc etc). Concensus mapping encodes the rich diversity
of the middle of the normal distribution curve and thus many methods of
interpretion still lead to the one 'fact'. e.g. X is west/left of Y.
As we shall see, this form of mapping enables us to have four basic methods of deriving the one 'fact' in QM.
We here take into consideration the prime dichotomy of prediction, me/universe. Having demonstrated the emergent states dealing with any dichotomy, we here consider the individual's attempts to detect external states and thus link inner reality with outer reality (note the dichotomy). We do this using a number of the most well known demonstrations of the apparent wave/particle nature of reality - the double-slit experiment using photons, the single-slit experiment using electrons, and photon polarization detection, as well as some more examples in Mathematics.
The double-slit experiment consists of the passage of a stream of photons first through a single slit in a barrier and then through a double slit in the same barrier. Detection equipment, in the form of photographic plates, positioned behind the barrier registers photons that pass through the slits.
With one slit open, the photographic plate shows a concentrated area where the photons have hit, but with both slits open the photographic plate shows an apparent interference pattern, banding, suggesting that there is a wave passing through both slits. However, when detectors are placed at the exit of each slit, they show that a photon passes through one slit or the other, not both.
This experiment is in fact the manifestation of a dichotomy, for what the double-slit experiment does is introduce the concept of choice, slit A/slit B, and this is a dichotomy and the time factor of allowing more than one 'test' (photon) introduces the dichotomy tree.
A passage through one slot traces out a path through time. This will appear as a 'normal' serial event, however, over time an interference pattern emerges. (I suggest that if we move the photographic plate further away, the banding becomes finer and we eventually get the 'uniform glow' found in the single-slit experiment - see below)
The single-slit experiment ia where a slit is made in a barrier and electrons are fired through the slit to hit a photographic plate placed behind the barrier. This experiement creates what is known as an Airy pattern and manifests the same behaviour as for the double-slit experiment in that the point of choice is between a point source and a uniform glow (we can extend this to a closed hole). This is determined by the width of the slit through which electrons pass. If the slit is large then we get the familiar concentrated area marking electron hits on a photographic plate placed behind the slit.
If the slit is almost closed we get a wide area of uniform distribution, or a uniform glow if photons are used onto a plain background. However, there is a point in-between these states where the interference pattern emerges over time (Airy derived a formula for this that depends on the width of the slit), Alastar Rae comments:
"If we perform this experiment with a very weak light so as to study the behaviour of individual photons, we find that - just as in the two-slit experiment - the photons arrive at the screen more or less at random, and the diffraction pattern is built-up gradually as more and more photons are accumulated." p10 (Rae 1994)
The fact that this emerges over time correlates with the generation of dichotomy maps in part I. Each dot on the photographic plate is a marker of context for it symbolizes what happened at time x, and the whole plate holds all previous contexts upto the decided time to stop. The plate becomes the manifestation of a dichotomy map.
Photons oscillate as they move. This is manifest as a transverse wave (sideways compared to the direction of motion.) The angle of the wave to the direction of movement determines what is called polarity; an oscillation left-to-right interprets as a polarization of 0 degrees, whereas an oscillation up/down interprets as a polarization of 90 degrees.
In this experiment it is found that, by creating a system where a photon travels through a horizontal bias filter, a filter that blocks photons of the left/right type, and then comes to a vertical bias filter, a filter that blocks photons of the up/down type, no photon is detected the other side of the last detector; the two detectors filter out ALL photons. BUT, by inserting a detector of varying angles inbetween the horizontal and vertical detectors, photons ARE detected the other side of the last detector.
The highest level of photon passage is achieved when the variable filter is set at 45 degrees - the mid-point of the 0-90 degree range. The dichotomy here is that of horizontal/vertical and the introduction of the third detector forces the creation of a dichotomy tree.
The main dichotomies here concerned are:
wave/particle
position/momentum (influence of the uncertainty principle).
slitA/slitB (double slit)
wide/narrow (single slit)
vertical/horizontal (polarization)
But it should be noted that in most of these experiments, the use of beam-splitting and down-conversion are examples of dichotomization within experimentation and could lead to the apparent interference patterns observed. This possible side-affect of dichotomization needs to be considered in experimentation.
In all experiments the systems show the traversing of all the possible dichotomy states inbetween the two 'extremes'. In the double slit experiment as well as the polarization experiment we find that the highest intensity is in the middle of the possible ranges, despite the fact that, for example, in the double slit experiment the two slits are to either side of this mid-point; one would expect the highest intensities to be at those points on the photographic plate directly opposite the slits.
The fact that this occurs supports the dichotomy map model in that, as Bateson has pointed out, and I have detailed, there is an oscillation in thought processing based on the dichotomy of FORM/PROCESS. When creating a dichotomy tree for this, an oscillation would create a higher chance of following the middle path than the extremes.
The question is, are these results 'real' or are they founded by our extending our senses through creating experimental apparatus? If the latter, these results would be expected considering the strong dichotomy bias in the experiments. As pointed out elsewhere, the instigation of a dichotomy opens-up, at best, a binary tree. The more detailed we get, i.e. many levels/many timeframes, the more 'wave-like' things start to appear. Our instrumentation is an extension of our sensory systems and as such will behave the same way; the fact that the detectable range is increased is irrelavent, for it is the methodology that is under inspection. In all three discussed experiments, we introduce choice (A or B), and even if there is no 'conscious' choice made, a dichotomy tree MUST emerge from this process when the experiment is extended past one event/moment in time.
The 'puzzle' here is that our instruments are outside of 'us', if I fire a stream of photons at two slits I do not expect the results to correlate with dichotomy analysis in the mind. What is suggested is that serialization, observed both internally and externally, is processed by the same neurology and thus strong analogies are possible between observed outer and inner, especially if the tools we use mimick our own senses.
However, introducing the dichotomy of inner/outer creates a tree and thus introduces various states combining inner and outer as well as two 'pure states' - this is where the Heisenberg Uncertainty Principle originates. As we go to more levels so the possible states between the two main dichotomy elements increases such that the absolute determination of a pure elemental state excludes the possibility of determining the other elemental state at the same time, especially at the micro-level. (At the macro level we can see both position and momentum of, say, a ball, but the more I concentrate on one element, so the more diffuse the nature of the other becomes - If I analize momentum, then position, which includes reference to background, becomes a 'blur').
QM demostrates our dichotomous form of mapping by having four main methods of symbolisation; just as there are four generic 'types'. These come from Feyman's Sum of Histories, Schrodinger's Wave Mechanics, Heisenberg's S-Matrix, and Dirac's Transformative Mechanics.
What is interesting is that the four methods of description can 'fit' the four cells at level 2 of the template. In other words, the four methods of description are related to the four fundamental roots of persona. Thus, at a very generic level, Feynman is biased to contractive blending, Dirac is biased to expansive blending, Schrodinger is biased to contractive bounding, and Heisenberg is biased to expansive bounding.
In the words of whole/aspects, Feynman and Dirac are biased to wholes, whereas Schrodinger and Heisenberg are more biased to aspects.
These four sub-metaphors demonstrate the underlaying structure of metaphor and how different personal interpretations can lead to the same results, since all four of these, to be successful within QM, must lead to the same 'objective' 'fact' that is 'out there'.