We live in an asymmetric universe but operate within that universe through the focus upon and use of symmetry. The benefit of this is through the development and maintenance of instincts/habits where THEIR use allows for quick assessments of differences as we filter them through sameness.
This conversion of difference to sameness comes with an artefact, a loss in precision and it is this loss that shows up in the realm of the symmetric in the form of a wave - and so the 'wave/particle' duality concept is born from attempts to impose symmetry on the asymmetric - as will be shown below.
Note that the focus on the symmetric DEMANDS the linking of elements into PAIRS such that a singleton is not allowed in that a singleton represent the asymmetric, and so in the realm of the symmetric everything has its 'complement' and so the focus is always on PAIRS and this takes us into the realm of dichotomies.
In the 'pure' form of a dichotomy, the Aristotle form, the symmetry is in the make-up of the elements of such a dichotomy as A/~A (NOT-A) or +1/-1 or positive/negative or left/right or front/back.
If we include the not-so-pure form, an asymmetric dichotomy, we allow for 'bifurcations' and the focus on difference/sameness as difference emergent from or being converted into sameness. Another dichotomy here is that of 'far-from-equilibrium'/'equilibrium'.
However, of note here is that the purely asymmetric is not open to recursion, we need a symmetric form and this is the first act of 'distortion'. In logic this is equivalent to converting the IMP operator into the XOR operator where both map 'difference' as the EQV operator maps 'sameness' but the XOR operator is symmetric in form (and so we recurse core same/same even when we represent difference/sameness)
We can apply the symmetric dichotomy to itself to elicit more categories than the basic A/~A. For ease of use, let us represent A/~A with the dichotomy of 1/0 and ITS self-referencing gives us:
1 / 0
11, 10 / 01, 00
111, 110, 101, 100 / 011, 010, 001, 000
Etc
Of note here is the sequence of bits that emerge left/right (or below as top to bottom) as I recurse the 1/0 dichotomy in that symmetry is not imposed top/down but also left/right.
Since we live in an asymmetric environment, the symmetrising of information comes in the form of 'disallowing' the asymmetric through change of representation into something dealable as if symmetric. Furthermore our focus is on PAIRS such that a sequence of 11 or 00 is allowable but 10 or 01 is not. This rule reflects the fact that in the realm of the symmetric the elements of a pair are interchangeable, order makes no difference to identification. This rule is fine for 11 or 00 but fails for 10 and 01. (to flesh this out a bit, the symmetric dichotomy of +1/-1 is rooted in sameness, 1/1 within which we focus on differences, +/-. Thus the root sameness is essential (gets into consideration of collections, classes etc in set theory etc))
A 'trick' of logic (and so mathematics and all rooted in set theory, which is richly focused on sameness in the form of sets) is that given 11 we can convert it 1, give 00 we can convert it to 0; there is no significance given to the two elements in the pair as 'one before the other' or 'one after the other', each 1 or 0 is identical with its other - in other words sequence/time is marginalised or more so the 'whole' is in the form of a PAIR rather than unit values - we have, as such, lost some sequence resolution.
So how do we handle 10 and 01? Since order make no difference at this level of the symmetric so both can be represented by X.
What is noticeable here is that whereas we have converted 11 to 1 and 00 to 0, we have packed 01 and 10 into X, 'two' differences into 'one' sameness.
If we now recurse the 1/0 dichotomy through six loops we will get 64 six-bit sequences of 0s and 1s to which we apply our symmetry rule leading to 'compression'. Thus, for example, we have:
001011 becomes 0X1.
000010 becomes 00X.
And so on.
As we go through the 64 combinations of bit patterns, and apply the symmetry rule, so some of our patterns once unique as six-bits take on shared forms with other patterns now as three-bit forms (interpreting X as a bit!) Thus 001011 and 000111 share the same form of 0X1. If we group the SAME patterns we end up with a property of symmetric perspectives, wave-interference. Below I have mapped the 64 six-bit sequences out in the form of sequences L and R, all from the L (left slit) / R (right slit) dichotomy (and so a symmetric format) to focus on experimental design issues where in the compression the LR and RL pairs are converted to X, as LL is to L and RR is to R:
(00) uncompressed - compressed
(01)LLLLLL - LLL
(02)LLLLLR - LLX
(03)LLLLRL - LLX
(04)LLLLRR - LLR
(05)LLLRLL - LXL
(06)LLLRLR - LXX
(07)LLLRRL - LXX
(08)LLLRRR - LXR
(09)LLRLLL - LXL
(10)LLRLLR - LXX
(11)LLRLRL - LXX
(12)LLRLRR - LXR
(13)LLRRLL - LRL
(14)LLRRLR - LRX
(15)LLRRRL - LRX
(16)LLRRRR - LRR
(17)LRLLLL - XLL
(18)LRLLLR - XLX
(19)LRLLRL - XLX
(20)LRLLRR - XLR
(21)LRLRLL - XXL
(22)LRLRLR - XXX
(23)LRLRRL - XXX
(24)LRLRRR - XXR
(25)LRRLLL - XXL
(26)LRRLLR - XXX
(27)LRRLRL - XXX
(28)LRRLRR - XXR
(29)LRRRLL - XRL
(30)LRRRLR - XRX
(31)LRRRRL - XRX
(32)LRRRRR - XRR
(33)RLLLLL - XLL
(34)RLLLLR - XLX
(35)RLLLRL - XLX
(36)RLLLRR - XLR
(37)RLLRLL - XXL
(38)RLLRLR - XXX
(39)RLLRRL - XXX
(40)RLLRRR - XXR
(41)RLRLLL - XXL
(42)RLRLLR - XXX
(43)RLRLRL - XXX
(44)RLRLRR - XXR
(45)RLRRLL - XRL
(46)RLRRLR - XRX
(47)RLRRRL - XRX
(48)RLRRRR - XRR
(49)RRLLLL - RLL
(50)RRLLLR - RLX
(51)RRLLRL - RLX
(52)RRLLRR - RLR
(53)RRLRLL - RXL
(54)RRLRLR - RXX
(55)RRLRRL - RXX
(56)RRLRRR - RXR
(57)RRRLLL - RXL
(58)RRRLLR - RXX
(59)RRRLRL - RXX
(60)RRRLRR - RXR
(61)RRRRLL - RRL
(62)RRRRLR - RRX
(63)RRRRRL - RRX
(64)RRRRRR - RRR
Reviewing the RIGHT column we find we have lost resolution power such that there are many duplicates. When we move
along this column, grouping the duplicates in the area of their duplication we get 27 groups - 8 of which have
one member each, reflecting a 'perfect translation', 19 are what can be called 'superpositions', different forms
now sharing the space due to the loss in resolution. Graph all of this, with the 27 groups mapped to letters of the alphabet + ZZ, (and so 000 = A, 111 = ZZ etc) and we get:
THAT is a wave interference pattern in the SAME form as we get in QM etc etc (we can use double slits, down converters,
polarisers etc etc - same method overall in eliciting POSSIBLE distributions)
If we take into consideration the XOR(difference)/EQV(sameness) dynamics of our brains in paradox processing,
so the LEFT column reflects XOR (unique entities) and the right column reflects EQV (sets). In such paradox as the Necker cube, the right
column is the 'complex line drawing' and the left column the two cubes we detect trying to share the same space.
This dynamic is not just limited to vision, it is also present in audition etc. and as such appears to reflect
a fundamental nature of our brains - XOR/EQV dynamics. THAT nature then gets into our experiment designs where we impose symmetry instinctively without
awareness of what we are doing, and we end up with 'paradox' where there is none.
ANY experiment set up in this fashion, with a method of storing the results will give us a 'wave interference'
pattern in the EQV position DERIVED from the XOR dynamics in the left column. The compression at work reflects the creation of 'superpositions' through conversion of difference to sameness as demanded by the use of a symmetric format in the design of the experiment.
An additional point being that as the left column is XOR to the right column's EQV, so each entry in the left column is an
EQV in its own right, reflecting the expression of ALL of the other entries in that column. This property is brought out here .
What this shows us is the implicit wave-ness still present in the seemingly discrete elements in the left column.
(the left column can be used to represent the left hemisphere of the brain as the right column can be used to represent the
right hemisphere of the brain- this left/right dichotomy of course applies all the way down the scale of the neurology, form
temporal/parietal dynamics in each hemisphere to axon/dendrite dynamics across the whole neurology etc)
Now move to the level of how we CATEGORISE and the XOR/EQV dynamic continues - be it in the MBTI or in human emotions
or in the I Ching or in types of numbers in Mathematics. (And so the IDM model of how
we derive meaning IN GENERAL)
No matter what level of recursion you are at, the imposition of symmetry to the set of elements recursed contribute to the expression of EACH
category, and that contribution is extractable using XOR/EQV dynamics - IOW there is a LOT more to categories then
just a sequence of 'types' that we then flesh-out ad-hoc, we do in fact have access to a spectrum of qualities
for each!
From the abstract level of the L/R dichotomy applied recursively, I can extract the '53-ness' of EACH category
in the above list using XOR/EQV processing. By this I mean that due to the entanglement of all qualities, this being a property of symmetry, so each
will reflect all others in some way or another. Thus pattern 53 contributes to the expression of each of the other
patterns and we can detect this - the WHOLE that is the XOR column is in fact COMPRESSED into the WHOLE that is
the EQV column. Our CONSCIOUSNESS is more associated with XOR dynamics (differences extended into the pure asymmetric as individuals) and as such is one step removed from the
EQV column that is representative of our integrated, compressed, species-nature.
The two columns show us the PRECISION issues we experience, where our left-column consciousness is more precise
than our right-column speciesness but in that precision thinks it is reality "AS IS" when in fact it
is reality "AS INTERPRETED". This bias feeds into our thinking in general about reality and so we can
create paradox where there is none. (as such "AS IS" reality is reflected in the photographic plate).
Those specialisations rooted in symmetric perspectives will themselves contain interchangeable perspectives - e.g. quantum mechanics comes with four 'different' forms of representations that can give the same results:
Dirac's Transformation Mechanics
Heisenberg's S-Matrix
Schrodinger's Wave Mechanics
Feynman's Sum of Histories
In all of these we find a main trait of symmetry - "all is connected" - as we do with interchangability of the elements of the wave/particle dichotomy and so another trait of symmetry - context dependence (and so 'local' vs 'universal' symmetries etc) - given the "all is connected" perspective so we have to focus on how we deal with paradox in that sensory paradox reflects the dynamics of metonymy, part-for-whole interpretations.
Given a bias to interpreting reality through conversion of difference to sameness, and so the asymmetric to the symmetric, and so the perpetuation of metaphors leading to the post-modern perspective of 'any metaphor will do', so careful consideration is required to delve deeper into reality and compensate for our symmetric focused heritage as instincts-dependent species through careful use of our asymmetric, and so unique, consciousness.