This website deals with how we humans derive meaning and then encode that meaning in our maps. This particular paper covers the possible confusion that can occur when in the process of map creation we encode properties of the METHOD of analysis as if they are properties of that which is under analysis. Physicists of the past have had little or no understanding of neurological function when in the process of making their maps and so lacked knowledge of these often implicit, unconscious methods and their properties. In this paper is demonstrated how the method of applying a dichotomy recursively, a method used by the brain to process data, can lead to the identification of frequency distributions of data suggesting wave interference at work. Thus a property of the METHOD of analysis has crept-in to quantum mechanics and been interpreted as a property of quantum mechanics; we have failed to identify (until now) the property as a manifestation of methodology, a methodology apparently sourced in our neurology.
Key words/phrases: Methodology, Quantum Mechanics, Wave/Particle Duality, Interference, Dichotomisations, Scale Invariance, Recursion, Neurology
A demonstration of, a commentary on, an emerging wave interference pattern solely from METHOD, here being the accumulation of all possible and actual choices made in selecting one element of a dichotomy (here we use 0/1, we can use left/right, up/down etc) over six trials. Thus the initial choice is 0 or 1. The second choice is 0 or 1, the third is 0 or 1 all the way up to the sixth, however any form of statistical analysis means that each choice is made WITHIN the measurement results set by the previous choices. The following diagrams emphasise this in that each trial reflects 2^n possible states in which to describe all results upto an including the current trial; n = number of trials. Thus from the first trial the value is 2^1 giving two possible outcomes, 0 or 1. The second trial have the same outcome but when we include the previous trial so there are 2^2 or FOUR possible outcomes generated by combining the previous with the next - 00, 01, 11, 10 and so on.
Therefore, each choice causes the unfolding of a binary tree of potentals through which weaves the thread of the actual choices made. By the time we get to trial 6 there are 64 states describing the possible choices made with one of the states manifesting the set of actual choices made. Trial 6 is the best trial to show the emerging distribution that reflects wave interference patterns. From trial 6 onwards the interference pattern just gets stronger in form.
Listing of all possible combinations of a 6 trial transition through a dichotomy mapped bottom-up.
final : 0101010101010101010101010101010101010101010101010101010101010101 0011001100110011001100110011001100110011001100110011001100110011 0000111100001111000011110000111100001111000011110000111100001111 0000000011111111000000001111111100000000111111110000000011111111 0000000000000000111111111111111100000000000000001111111111111111 initial: OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO11111111111111111111111111111111
I have colour coded (green) one path through this set of potentials to emphasise the thread of actual choices made. Thus the path is 010011 (or left/right/left/left/right/right, up/down/up/up/down/down etc etc).
Listing of all possible combinations of the same 6 trial transition through a dichotomy mapped bottom up BUT with the inclusion of a distortion where 01 or 10 transitions represent 'unknown' states and are marked as X. Due to the collapse of 01 and 10 to X so we also collapse all 00 states into 0 and all 11 states into 1. This process mimics the experiments in quantum mechanics, especially the double slit experiment, where once we stop measuring directly at the slits so we cannot identify precisly WHICH slit a particle went thorough for each trial. This reflects a 'BOTH/AND' state. Laser interferometer experiments also map the 00 to 0 and the 11 to 1.
final : 0XX10XX10XX10XX10XX10XX10XX10XX10XX10XX10XX10XX10XX10XX10XX10XX1 0000XXXXXXXX11110000XXXXXXXX11110000XXXXXXXX11110000XXXXXXXX1111 initial: 0000000000000000XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX1111111111111111
Note how in the above there are now TWO possible paths that reflect the orginal 010011 pattern now compressed into X01.
Graphing of all LIKE patterns identified in step 2. In other words all bottom-to-top columns that have the SAME formats (e.g. all with X01 as bottom-to-top order) are counted and grouped.
This process compresses the 64 unique columns from step 1 into 27 unique columns. For each of these unique columns we identify the number of columns that were mapped into the unique column, in other words we list with each unique column the total number of copies in the stage 2 listing. e.g. in the stage 2 listing, from the left, columns 2 and 3 are identical bottom-up (00X) thus we have a unique form (00X) and associate the number 2 with it representing the number of copies in the step 2 listing.
Here is the listing of the 27 unique columns and their associated numbers (the compressed X01 is marked in green, the total number of copies in red):
Unique Columns : 0X10X10X10X10X10X10X10X10X1 000XXX111000XXX111000XXX111 000000000XXXXXXXXX111111111 No. of Copies : 121242121242484242121242121
If we graph these numbers we see emerge a wave interference pattern:
Note that in this pattern there are eight states that are invarient, reflecting the troughs in the wave pattern where there is at least 1 entry.
The above demonstrates that encoded within the METHOD of using dichotomisations to map reality are expressions of wave interference regardless of what is being measured - use recursive dichotomisations and add indeterminacy, as we find in quantum mechanics, and you 'get' wave patterns; the structure of the experiments mimic recursive dichotomisation.
All experiments based on dichotomisations will give results compatable with the limits, the properties, of the METHOD. This does not necessarily mean that these results are 'out there' but more so that within the context set by the method, that context includes 'wave' patterns.
Also note that in step 2 there is a distortion in that the often 'casual' mapping of sameness elements, i.e. 00 and 11 to 0 and 1 misses the point that a 01 or 10 state is BOTH/AND but a 00 or 11 state is pure, is EITHER/OR. This sort of categorisation can cause problems.
Finally, note that there is a fundamental distinction here between the particular and the general. When you put detectors at the slits you get EITHER/OR mapping; only when you move away to do statistical analysis you lose resolution of the elements of the slits, by this I mean that a statistical analysis works with a minimum unit of PAIRS and the ORDER of the elements in those pairs becomes unknown; you have moved to the scale of the general.
Movement from a scale of the particular to the general reflects a change in expression from ordinal to cardinal; the use of probabilities expressed as waves reflects a more cardinal perspective of size as manifest in the wave amplitudes.
For a general map (.gif file) of ordinality/cardinality sourced in our neurology, where our brain/mind/culture manifest generalisation of the neuron structure and function, click here
