...life can be translucent


Discrete from the continuous


Mar 16, 1970
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Recent work in the context of the XOR (Exclusive OR) operator and its operation in our brains has indicated that the focusing of attention bounds ?something? and recursion of the differentiate/integrate (aka WHAT/WHERE) dichotomy within that bound allows us to come up with qualities usable to describe that ?something?.

In the realm of differentiating, the ability to use XOR introduces us to a requirement for that operator to function ? recursion. This requirement is due to the need for TWO neurons to implement XOR ? one feeding back upon the other. This SAME mechanism is required for a basic memory system and as such we can associate recursion with precision as well as discreteness and, overall, with the encoding of meaning as memories etc.

Due to the encapsulation by the attention system of ?something?, so the set of qualities usable to derive meaning is in the form of a bounded spectrum (e.g. as the visible light spectrum is a part of the whole EM spectrum but is a ?whole? for our senses; this also applies to all other senses).

This spectrum becomes the source of the ?language? used to describe reality ? where recursion allows for the making of finer distinctions in the spectrum but not exceeding that spectrum. (that said, our mediation has allowed us to create technology that ?transcends? that spectrum, giving us access to the extremes not possible directly)

Each distinction in that spectrum is associated with a quality, a feeling, derived from neural dynamics, used to describe ?reality? and as such the spectrum is the foundation for language processing through the use of the qualities and, later on, their relabelling to fit unique contexts. (The developing indication here is that we communicate through spectrum exchange that allows for ?resonance?)

Further work with the XOR (exclusive OR) operator has shown that given a finite language so each ?part? of that language is not ?discrete? but more so an exaggeration of an aspect of the language and as such contains the whole within it in the form of harmonics.

We can see this if we use the wave metaphor where each level of recursion is a waveform. (For a diagram see http://www.iimetro.com.au/~lofting/myweb/btree.gif)

As we recurse so we are creating a superposition where each level encodes its wave-nature into the same meaning-space with other waves such that after, say, six levels we have six waves summed into one expression ? where constructive/destructive interferences elicit that particular expression and each level of recursion is representative of a higher frequency than the previous level(s).

Since we are moving from general-to-particular in recursing a dichotomy, the encoding at level 6 is where we have 64 qualities of potential meanings made up of different phases of waves of frequencies of:

2cps (low freq ? general, vague ? two qualities, yin/yang)
64cps (high freq, particular, crisp ? 64 qualities)

In this ?meaning? space, the realm of POTENTIALS is when none of these waveforms are actualised. The MAXIMUM actualisation is when ALL waves are present, where all of the rest come out in the range of the 64 possible patterns. As such, these patterns are our ?language? with which we interpret reality. Since there is no way we can achieve a 1:1, literal, mapping of reality so we have to use the same set of qualities as our source of analogy/metaphor ? in other words most of what we communicate is figurative.

For any moment, ALL of the potentials are valid but ONE will be favoured and so the potentials get sorted into degrees of ?actualisation? ? from best fit to worst fit ? for that particular moment.

If we represent these wave levels using bits (0/1) then with 6 levels we have a sequence of bit patterns from 000000 to 111111 where each bit represents the presence (1) or absence (0) of a waveform, ordered from general to particular and the sum reflects an overall expression.

My research shows that in this form of derivation (recursion) and representation (qualities from the recursion), EACH of the 64 patterns contains ALL of the others in the form of ?harmonics? that affect the expression of that pattern.

In the brain we see this use of harmonics in interpretations of data, where one harmonic is the ?fundamental? and all others work within that harmonic. This dynamic is reflected in the FM/AM operations of the brain ? reflecting the XOR/AND dynamics of categorisations, the axon/dendrite dynamics of neurons (and it is the common theme of music with a key and harmonics)

This sequence of harmonics derived using XOR is reflective of a ?genetic code? of each pattern. Where, given the 64 possible patterns, interpreted as archetypal qualities of meaning, if we XOR any archetype with one that is setting a context we will extract the expression of that archetype THROUGH that context in the form of an analogy with one of the other archetypes.

For example, given a context described by 111111 and an archetype quality of 100001: if I XOR 100001 with 111111 I get 011110. This quality describes the 100001-ness of 111111. This may seem ?meaningless? without more concrete examples, so I have derived two sets covering two specialisations I use as examples of the IDM generalisation that is ?beneath? our expressions. These examples are:

(1) MBTI ? see http://www.iimetro.com.au/~lofting/myweb/type.html
(2) I Ching ? see http://www.iimetro.com.au/~lofting/myweb/linemean.html#Details

What is implied here is that we are not dealing with discrete forms in our categories, we are dealing with a superposition where CONTEXT elicits the ?preferred? expression, draws out an ordering of frequencies to give us what we perceive ?discretely?, and sorts all of the others forms into expressions of their archetypal forms through this particular (in a bestfit/worstfit ordering). Thus in EACH quality we can extract the expression of some other but usually in the form of an analogy.

When applied to the categories of the MBTI, for example, there is a LOT going on in those personas that is ?hidden? from the usual form of categorisation, where we recurse to a row of categories and stop there ? supplementing the categories with narratives. The recursion is in fact not ?discrete? and so elements of behaviour of a category are extractable using XOR, to give us a ?full spectrum? of that persona.
The basic requirement here is for the ordering of categories to be in a spectral format ? be it sorted by energy differences (temperatures) or some other ?power law? pattern.

Due to the methods of recursion, working on the universal template for dichotomies, based on differentiating/integrating, will recurse that asymmetric dichotomy into a spectrum format. We can then overlay this universal with labels that associate the universals with local context.

For example, in the I Ching we associate lines of yin/yang with this spectrum of meaning. We do the same form of associations with categorising personas (MBTI) or with basic human emotions, or with types of numbers used in Mathematics. (see IDM perspective in deriving the format ? http://www.iimetro.com.au/~lofting/myweb/idm001.html)

Another form of dichotomy, the symmetric, reflects the focus on a particular level in a hierarchy where the same-level-nature elicits the form of SAMENESS in its members and the dichotomy is focused on extracting DIFFERENCE from the sameness (e.g. IQ scores of people).

This focus on difference within sameness will be highly differentiating, competitive, in that the aim is to maximise the difference in the sameness. (The asymmetric dichotomy extracts sameness across differences, as we cover in this article with identifying the sameness across specialisations and so identify the sameness in ?differences?)

Behaviourally, the realm of the competitive is the realm of the differentiating, aka of what the Chinese label as YANG. This reflects a bias to differentiating, high-energy expenditure. High-energy expenditure indicates high frequency processing. High frequency processing indicates short wavelengths. Short wavelengths indicate a susceptibility to being easily ?scattered? ? and so the precision, the purity is always ?unstable?, fragile, and so an idealisation of ?reality?.

(Note that the FM nature in our brains reflects the clarity in experience but also the short range, line-of-sight nature and so ease in losing the signal etc ? expressed mentally gets into the sense of taking things literally, lack of skills in seeing ?behind? things, in dealing with innuendo, ?filling in the dots? etc (the argument being we use the SAME set of qualities used to process sense information as we do using mental information ? the brain makes no distinctions in that it works with frequencies, wavelengths, and amplitudes, period.))

In our brains the LAST part to develop is our frontal lobes area. This is the area of a developed sense of consciousness, of mediation and so planning. It reflects a form of ?imprinting? of current social context and is the ?home? of the rational, where links to older parts of the brain allow for the DELAY in expression of some instinct/emotion. This delay reflects the nature of consciousness as mediating, use of recruitment etc of areas/memories to increase bandwidth etc to resolve issues. (damage to these areas can elicit ?anti-social? behaviours where the repression element malfunctions)

BUT, this area is also prone to ?issues? ? such as ADHD etc. (possibly related to the ease in scattering of short wavelengths ? and imprinting of a high-precision culture could bias things to that perspective overall ? short attention spans but also high bandwidth focus, communications using archetypes/stereotyping etc etc ? these areas need to be TRAINED, not left to develop ?ad hoc?. The training elicits control of the suppression elements present in these areas and makes things ?instincts?-driven more efficient).

The difference between an instinct and a memory is that the former is a ?pattern? of reply to a stimulus, is immediate. Memory is more an association with mediation dynamics where CHOICES of memories on offer allows for a selection of one to ?fit? as a response, or to aid in developing a response, to some novel experience. As such, memory access is DELAYED when compared to the immediacy of an instinct/habit (the reflex arc being a classic example of ?mindless?, immediate, response to a stimulus)

The focus on precision associates the XOR operator with overly differentiating dynamics and with that precision comes the emergence of the IMP operator, the only asymmetric operator in the set of tools available to process information ?logically?. The asymmetry develops naturally when given an XOR/AND aka differentiating/integrating context, as found in our brains, such that the IMP operator is ?natural? and reflects ?in here? just as much as all of the other logic operators do. (?and that includes time-dependent operators derived from dialectical logic).

If we accept evolution then our neurology reflects the adaptation to the environment and so to the universe in general ? we have internalised the information-processing dynamics of ?out there? in the form of our neurology. As such, all of the logic operators ?in here? reflect dynamics of ?out there?, OTHER THAN XOR and IMP. IOW recursion can be ?out there? but the use of XOR to extract particular information transcends recursion and XOR is delayed in its development ?in here? and so later in its evolution than the more basic AND/NOT etc operators.

XOR/IMP allow us to extract PARTS from a WHOLE and in our brains the XOR areas are the LAST to develop, be they frontal lobes (late development) or left hemisphere (early development but later than the right. Michael Gazzaniga?s labels for these hemispheres are left = ?AS INTERPRETED?, right = ?AS IS?.)

The UNIVERSALISATION of limb use etc, combined with our creation and use of universals in the form of labels, are all associated with the differentiating parts of our brains ? in particular the left/right hemispheres where the one that takes on the high precision focus is also the one that takes on universal limb-ness and management of labels (discreteness of the spoken/written word etc). In MOST of our species, this universalisation bias is to the LEFT hemisphere (and so right handedness, Broca?s area etc etc etc) ? for more on this read such texts as Goldberg, E., (2001) ?The Executive Brain : Frontal Lobes and the Civilized Mind?.

This focus on precision, on purity, etc., reflects an EXAGGERATION of the ?species-nature?, the more ?right brained? dynamics (aka the more integrating dynamics) where the instinctiveness, the vagueness, the ?everyday-ness?, the ?autopilot?, of that realm is aided in dealing with reality through the skills attainable using our differentiating skills (and so ?left? biases in precision. Note that we are in fact dealing with an integration of left-right and front-back dimensions, each reflecting a spectral pattern from low frequencies [right and back] to high frequencies [left & front]).

This asymmetry in hemispheres is sourced in lower life forms where the distinctions of the KNOWN from the UNKNOWN, the CRISP from the VAGUE, the PRECISE from the APPROXIMATE, is reflected in the brain structures of those lower life forms (e.g. the tiny zebra fish has this asymmetry in its ?primitive? brain and distinguishes known from unknown).

The main difference between us and ?lower? life form is the increased complexity that allows for us to derive universals to communicate to others and to represent reality and pass those representations on to future generations ? IOW we have ?transcended? the local known/unknown dynamics to move into universals in handedness as well as in communications ? all reflecting a drive to universalise and so adapt perfectly to any context, just needing a ?couple of days? to get the local nuances to aid in that ?fitting in?.

The asymmetry discussed is across all dimensions we use in interpreting brain dynamics ? e.g.

Temporal-lobe/Parietal-lobe (both sides)
Front temporal/back temporal
Ventral paths/Dorsal paths
?dot? precision/?field? precision

Recursion of dichotomies gives us finer details ?skewed? by the general categorisation, and so the duality we can experience. Thus, given above, we have integrating as the right element but zooming-in we also have:


IOW WITHIN what has been differentiated we find operating integration in the form of links of PARTS etc to give us the wholeness of what has been differentiated. (as such parts of parts). This moves us into considering hierarchy.

These dichotomies are synonyms for the differentiating/integrating dichotomy being applied to specialist perspectives (and so being relabelled to express that perspective).

The hierarchy in this is covered in the differences of differentiating/integrating where ALL of the above reflect generic asymmetric dichotomies in that the LEFT element has emerged from the RIGHT element; or more so is a CONCENTRATION, particularisation, of that right element ? e.g. SYNTAX and SEMANTICS both cover ?meaning? but the more ?left? we go so the more we focus on dynamics WITHIN something.

In the above dynamic, so the increase in precision using XOR/differentiating takes us deeper into what has been originally differentiated ( the ?whole?) and so we move into the realm of parts and their relation to the whole ? IOW their POSITION in the hierarchy. Here we are not only dealing with XOR but also with IMP. With this focus so the ONLY thing that is ?unconditionally? meaningful is one?s position in relation to all others ? and so all meaning is concentrated into what we label as SYNTAX.

Thus semantics is GENERAL, syntax is PARTICULAR. Given a ?differentiation? such as a ?meaning?, so that meaning has parts in a specific, and so syntax-focused, format ? integration is now within what has been differentiated.

This focus on high precision and so discreteness hides the underlying nature that is ?wave? or ?pulse? oriented. In that hiding is the element that reflects the linkage of us all together as a species and that species with this planet. The XOR operator, through the IDM mapping of recursion of dichotomies, allows us to extract parts from parts and in fact, through the existence of that dynamic, identify the ?holistic? nature of our being ? beneath all of the competition we are in fact ?one?.



Dec 29, 1972
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Too long to read esp. when i am busy.

Is your XOR is a scientific term for "vertical thinking" in the book by Edward de Bono?

I love the book "Lateral thinking". That really make me AND-oriented.


Dec 29, 1972
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Since we are moving from general-to-particular in recursing a dichotomy, the encoding at level 6 is where we have 64 qualities of potential meanings made up of different phases of waves of frequencies of:

2cps (low freq ? general, vague ? two qualities, yin/yang)
64cps (high freq, particular, crisp ? 64 qualities)

2cps - a reflection of reality without personal preference

4cps - a resonance, an impulse?

8cps - some thinking ...

16cps - heavy thinking and comprehension

32cps - convertion of brain dynamics to our muscles

64cps - a distillation of both mental and physical world!

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