The fourth postulate is the most important of Non-Euclidean, ¡logic geometry, as it defines the behavior of T.œs, organic points in its relationships to other points, establishing the fundamental law of duality: parallels, are similar beings which maintain a constant flow of communication forming herds and social organisms; different beings enter in darwinian relationships in perpendicular events in which they destroy each other.
FOREWORD. THE I-LOGIC POSTULATES: 4th and 5th:
MINDS-MONADS THAT COMMUNICATE ACCORDING TO SIMILARITY
A case of Darwinian devolution among men that perceive each other as different and enter into a perpendicular, Darwinian relationship and a case of social evolution between 2 forms that perceive each other as equal and enter into a parallel relationship of social love. The fourth postulate of non-Æ topology thus ‘vitalises’ the laws of mathematics, establishing the three fundamental geometrical≈behavioural relationships between T.œs, according to its:
- Informative (Particle-head) communication, possible in cases of relative similarity≈parallelism (which determines parallel herding and social evolution).
- Perpendicularity≈difference in particle-head, which will determine if one system is related to the other and there is body-similarity, hence can be used as energy its darwinian destruction,
- Or IF THERE IS NO similarity NEITHER IN BODY OR MIND, its existence as ‘cat alleys’, that never cross (relative invisibility). We talk then of Skew T.œ.s.
Indeed in three-dimensional geometry, skew lines are two lines that do not intersect and are not parallel. It follows that two lines are skew if and only if they are not coplanar, which IN 5Ð AS 3 ±¡ planes co-exist in the same organism and systems feed in T.œs, two super organisms down, IMPLIES SPECIES which are not in the relative planes of action of the being.
The different degrees of Parallelism, Perpendicularity and skewness are thus essential concepts of vital Non-Euclidean geometry.
And as all has degrees of ‘grey’, it is also a relative concept and essential to many branches of sciences, notably quantum physics to know the relative angle of parallelism, perpendicularity and skewness (here we redefine the concept NOT using it only for probability theory), of a system (and to make things more complex in which type of geometry, of the 3 ‘analytic points of reference’ – Hyperbolic, euclidean, polar & complex or lineal=cylindrical we are talking of)…
All those are hints for future researchers. We won’t be so detailed.
In the jargon of 5Ð specially to study physics, we also use for those 3 concepts, the concepts of a(nti)symmetries:
We have introduced in the graph with a bit more of complexity the logic dimensional laws that define how systems IN ANY scale of the inverse, from Atomic Ions or crystals to human societies relate to each other in darwinian, perpendicular ‘tearing’ topological relationships that ‘break’ the closing membrane of one species disrupting its existence, or will keep a mean distance to form social networks of communication that will grow into super organisms, starting the emergent process of evolution of species into a new ∆§cale of social existence, so you understand that in the Universe organic, geometric and scalar relationships are symbiotic to each other.
In the graph, symmetry is close to parallelism reason why social systems evolve into symmetry forming herds. Dysymmetry is a mirror form of parallelism, or ‘inverse parallelism’, which is complementary and needed to form pegged ‘genders’, bilateral systems, etc.
Antisymmetric forms are therefore the perpendicular ones, and its Darwinian relationships are also essential.
Asymmetric systems on the other hand are NOT equal to Skew systems, but is the closest concept. Why we do NOT have another ‘concept’ for Skew systems IS FOR THE SAME REASON ORGANISMS CODE ONLY 4 DIMOTIONS (4 quantum numbers, 4 genetic numbers, 4 Human dimensions of spacetime, etc): BECAUSE entropy=death and Invisible beings that do NOT relate to us, are of NO importance.
Still this Asymmetric concept is intuitively perceived as ‘skewness’ in probability where the distortion of a bell curve is the measure of its skewness:
We use then for the fourth form of relationship between entities through its actions – in this case the non-relationship, ‘skewness’; the fourth set of cards, the trebol, meaning the ‘fourth invisible leaf’ of a trebol, we don’t see, might not exist, is that cat alley of dark spaces of the Universe, between the networks of similar knots we know because they are either social, parallel to us, Darwinian enemies or complementary genders.
Skewness though is more profound that it might seem, as it sometimes means merely the disguising of a predator form, either at individual level, or at network level, specially when a language of information, for example, gravitation in the galaxy, money in social systems, is invisible or incomprehensible for the other species from where it will extract energy without realizing. Skewness is structurally also a form of space, which reaches in hyperbolic systems its maximal strength…
As all the themes teated in this blog, it has much more ‘meat’ of what it seems at first no-sight.😜